Robust Kernel Nonnegative Matrix Factorization

Zhichen Xia, Chris H. Q. Ding, Edmond Chow

Abstract: Kernel methods and Nonnegative matrix factorization (NMF) are both widely used in data mining and machine learning. The previous one is best known for its capability of transforming data into high dimension feature space, while the latter one is well known for its natural interpretations and good performance. In this paper, we propose a robust kernel NMF approach using L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2, 1</sub> norm loss function. Compared with the standard NMF algorithm, the new robust kernel NMF updating algorithm is as elegant and as simple, but with the newly added robustness to handle significantly corrupted datasets because of using L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2, 1</sub> norm. Experiments on normal and occluded datasets indicate that robust kernel NMF always perform better than k-means and standard NMF.